Project #7: Exploring White Wines

Data Transforms: Quality Score

From the structure table above we see that the quality score is defined as an integer variable. By transforming this to a factor variable we will be able to use it in later plots for classification; this new variable is added to the dataset.

## 
##    0    1    2    3    4    5    6    7    8    9   10 
##    0    0    0   20  163 1457 2198  880  175    5    0

Quality

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.000   5.000   6.000   5.878   6.000   9.000

## 
##     6     5     7     8     4     3     9     0     1     2    10 
## 0.449 0.297 0.180 0.036 0.033 0.004 0.001 0.000 0.000 0.000 0.000

The output variable, quality - a score from 0 (very bad) to 10 (very excellent) - follows a normal distribution, with the large majority in the 6 and 5 range. The proportions, sorted, for each of the quality scores is shown below the summary.

Alcohol

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.00    9.50   10.40   10.51   11.40   14.20

The distribution of alcohol in white wines ranges from 8 to 14 percent alcohol by volume, and has a very positively skewed shape. This may be a factor of an unbalanced dataset with a large proportion of dry wines that are low in residual sugar (as can be seen in the following plot).

Residual Sugar

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.600   1.700   5.200   6.391   9.900  65.800

The plot for residual sugar shows a positively skewed distribution with a very long tail, all data points. Transforming the data on a log10 scale results in a bi-modal distribution with a peak at around 1.1 and another at around 9.

## 
##        Dry Medium-Dry     Medium      Sweet 
##       2097       1975        825          1

##        Dry Medium-Dry     Medium      Sweet 
##      0.428      0.403      0.168      0.000

## df$sweetness.level: Dry
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.600   1.300   1.600   1.823   2.200   4.000 
## -------------------------------------------------------- 
## df$sweetness.level: Medium-Dry
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.100   5.800   7.500   7.641   9.300  12.000 
## -------------------------------------------------------- 
## df$sweetness.level: Medium
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   12.05   13.10   14.45   14.94   16.20   31.60 
## -------------------------------------------------------- 
## df$sweetness.level: Sweet
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    65.8    65.8    65.8    65.8    65.8    65.8

pH Level

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.720   3.090   3.180   3.188   3.280   3.820

The pH levels range from 2.72 to 3.82, with the mean and median almost the same, at 3.180 and 3.188 respectively. The plot shows a classic normal distribution.

Fixed Acidity

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.800   6.300   6.800   6.855   7.300  14.200

Fixed acidity (FA), which measures tartaric acid, follows a normal distribution and there are a couple of outliers in the right-hand tail.

Citric Acid

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.2700  0.3200  0.3342  0.3900  1.6600

Citric acid, which is added to improve “freshness”, has a normal distribution and several outliers beyond 0.75 g/dm³ in the right-hand tail, and a spike at just under 0.5 g/dm³.

Volatile Acidity

According to the Code of Federal Regulations (CFR), the allowable limit for volatile acidity (VA) is 1.1000 g/L ³. High levels of VA can lead to a vinegar taste, which is considered a wine fault; many people can detect this at levels above 600 mg/L ⁴, or 0.6 g/L.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0800  0.2100  0.2600  0.2782  0.3200  1.1000

The first plot for volatile acidity (VA), measuring acetic acid, has a pronounced right-skew and a long right-hand tail. Transforming the variable to log10 scale reveals it’s a log-normal distribution!

The summary shows the max VA value to be 1.1000 g/L, which falls within allowable limits.

##  low_VA high_VA 
##    4825      73

##  low_VA high_VA 
##   0.985   0.015

##     quality     
##  Min.   :3.000  
##  1st Qu.:5.000  
##  Median :6.000  
##  Mean   :5.891  
##  3rd Qu.:6.000  
##  Max.   :9.000

##     quality     
##  Min.   :3.000  
##  1st Qu.:4.000  
##  Median :5.000  
##  Mean   :5.014  
##  3rd Qu.:6.000  
##  Max.   :8.000

Sulphates

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2200  0.4100  0.4700  0.4898  0.5500  1.0800

The first plot for sulphates appears to have a slightly positively skewed normal distribution. With a log transform we have a log-normal distribution.

Total Sulfur Dioxide

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     9.0   108.0   134.0   138.4   167.0   440.0

Total sulfur dioxide looks to be normally distributed, but there are a number of outliers in the right-hand tail.

Free Sulfur Dioxide

Sulfur dioxide is important for keeping wines fresh, however, levels of free sulfur dioxide over 50 ppm can be sensed and are undesirable.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.00   23.00   34.00   35.31   46.00  289.00

Similarly, the distribution for free sulfur dioxide has a very slight positive skew with several outliers in the tail. The vertical line at 50 ppm (ppm is equivalent to mg/L), indicates the concentration at which free sulfur dioxide becomes noticeable in the smell and taste of the wine. In the second plot I’ve set a limit to zoom in on the bulk of the data points.

##  low_SO2 high_SO2 
##     4030      868

##  low_SO2 high_SO2 
##    0.823    0.177

##     quality     
##  Min.   :3.000  
##  1st Qu.:5.000  
##  Median :6.000  
##  Mean   :5.915  
##  3rd Qu.:6.000  
##  Max.   :9.000

##     quality     
##  Min.   :3.000  
##  1st Qu.:5.000  
##  Median :6.000  
##  Mean   :5.705  
##  3rd Qu.:6.000  
##  Max.   :9.000

Chlorides

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00900 0.03600 0.04300 0.04577 0.05000 0.34600

The distribution for chlorides is normally shaped, but with a very long tail of outliers beyond 0.075 g/dm³. Zooming in we get a better look at the normal distribution.

Density

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9871  0.9917  0.9937  0.9940  0.9961  1.0390

The distribution for density is not very dispersed, but also has several outliers. This attribute is a function of several other variables, mainly residual sugar and alcohol (as will be seen in the correlation matrix below).

What is the structure of your dataset?

There are 4898 white wines in the dataset, with values for 11 attributes and 1 output variable. All attributes and the output (quality) are numeric values.

Observations based on attributes:

• The most common quality ratings are 6 and then 5, accounting for 45% and 30% of the wines respectively.

• Most wines in the dataset have low residual sugars: they are classified as Dry (<4 g/L) or Medium-dry (<12 g/L) wines. These wines account for 42% and 40% of the wines respectively.

• The median value for alcohol (% by volume) is 10.4, and the mean is just slightly higher at 10.5. The interquantile range (IQR) is from 9.5 to 11.4.

• Almost 18% of wines have a free sulfur dioxide level greater than 50 ppm.

• Only 1% of wines have higher VA levels above 600 mg/L.

What is/are the main feature(s) of interest in your dataset?

The main features of the dataset appear to be alcohol, residual sugar and density. These attributes are highly correlated (seen below in the correlation matrix of the Bivariate Plots section), as alcohol is a byproduct of the fermentation process. I would like to see whether there are any other variables that may have an impact on these features or the quality score.

What other features in the dataset do you think will help support your investigation into your feature(s) of interest?

From the correlation matrix in the Bivariate Plots section we see that the strongest correlations are between density and residual sugar, and then with alcohol; this is as I expected (fermentation process).

There also is a moderate correlation between total sulfur dioxide (SO2) and density, as well as with alcohol. As total SO2 also contains the free SO2, and it is this free form that is detectable, I will add this to the features of interest.

Did you create any new variables from existing variables in the dataset?

I created a factorised variable for sweetness level based on the sweetness categories “Dry”, “Medium-dry”, “Medium” and “Sweet”.

I created a simple factorised variable for high/low volatile acidity (VA) levels; acetic acid can be detected in wines as a vinegary taste, and this may have an effect on the quality score.

I also created a similar factorised variable for high/low free sulfur dioxide (SO2) levels; this can also be detected as an unpleasant smell and taste. Likewise, higher levels of this attribute may affect the quality score.

Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?

The distribution for residual sugar is heavily skewed and oddly shaped, and the majority of wines have small levels.

I created a factorised version of the quality score; the original variable remains unchanged. This factor variable makes it easier to create boxplots with other variables.

I also plotted a log-transform for residual sugars; the transformed distribution is revealed to be bi-modal with a peak at around 1.1 and another at around 9.

Plotting a log-transform for volatile acidity as well as sulphates also revealed log-normal distributions.

Simplified Quality Categories

First, I’ll create a new variable with 3 factors based on quality, so the bins are more similar in size.

poor [0-5], good [6], and excellent [7-10]

## 
##      poor      good excellent 
##      1640      2198      1060

##                             [,1]
## fixed.acidity        -0.10315405
## volatile.acidity     -0.18292444
## citric.acid          -0.02030053
## residual.sugar       -0.12550624
## chlorides            -0.22131592
## free.sulfur.dioxide  -0.01397733
## total.sulfur.dioxide -0.20118454
## density              -0.33249501
## pH                    0.10642160
## sulphates             0.06002660
## alcohol               0.46316492
## quality               0.94906065

Correlation coefficients for the simplified quality levels aren’t much different from the original quality scores.

Quality vs. Alcohol

Both of these plots show a distinct relationship reflecting the moderate, positive correlation between alcohol and quality, with a coefficient of 0.44. The wines with higher quality scores seem to have higher levels of alcohol.

Now using the simplified quality level - poor, good and excellent - let’s see how the poor and excellent compare.

## df$quality.level: poor
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.00    9.20    9.60    9.85   10.40   13.60 
## -------------------------------------------------------- 
## df$quality.level: good
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.50    9.60   10.50   10.58   11.40   14.00 
## -------------------------------------------------------- 
## df$quality.level: excellent
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.50   10.70   11.50   11.42   12.40   14.20

The plot with the combined, simplified quality levels shows the difference in distribution between the poor and excellent quality wines. The median alcohol level for poor wines is much lower than for the excellent wines, and the 75th quantile for poor quality level wines (quality 0 to 5) is even slightly below the 25th quantile for excellent quality wines; the overlap between poor and excellent is small.

Quality vs. Density

When removing the 3 extreme outliers, shown above the blue line at 1.005 in the first plot, and zooming in, it seems like there is something of a relationship between quality and density. Despite the look of it, the correlation is weak, with a coefficient of just -0.31.

## df$quality.level: poor
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9872  0.9932  0.9951  0.9952  0.9971  1.0024 
## -------------------------------------------------------- 
## df$quality.level: good
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9876  0.9917  0.9937  0.9940  0.9959  1.0390 
## -------------------------------------------------------- 
## df$quality.level: excellent
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9871  0.9905  0.9917  0.9924  0.9936  1.0006

The violin plot, with the 25th quantile, median and 75th quantile, shows quite well how the distributions for density differ between poor and excellent quality wines.

Quality vs. Residual Sugar

The first plot, containing all data points, includes some extreme outliers making it difficult to see the detail. In the second point plot I’ve set an upper limit of 23 g/dm³ on residual sugar (RS) to exlude those extremes, and now we see the variation among the quality factors. The slight downward slope of the smoothing line indicates little correlation, reflecting a coefficient of -0.10.

Let’s see how the distributions for RS compare between the simplified quality level variables, poor, good and excellent.

## df$quality.level: poor
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.600   1.700   6.625   7.054  11.025  23.500 
## -------------------------------------------------------- 
## df$quality.level: good
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.700   1.700   5.300   6.442   9.900  65.800 
## -------------------------------------------------------- 
## df$quality.level: excellent
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.800   1.800   3.875   5.262   7.400  19.250

## 
##  Pearson's product-moment correlation
## 
## data:  as.numeric(df$quality.level) and df$residual.sugar
## t = -8.8518, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1529750 -0.0978437
## sample estimates:
##        cor 
## -0.1255062

When using the simplified quality levels, there isn’t much of a difference in correlation coefficient, -0.13 here. We do, however, see a difference in variation between the levels: the median residual.sugar levels and the variance for excellent quality wines is less than for poor wines.

Density vs. Alcohol

This plot shows a very tight concentration on the left, but then an outlier that is so far removed from the rest. Is this outlier valid data? I’ll remove this one, and the next 2, from the next plots.

Subsetting the dataset eliminates the 3 outliers, and we can see the strong relation between alcohol and density, echoing the correlation coefficient of -0.78. It looks like wines with a higher density have lower alcohol levels.

With a reverse transform on the y-axis (alcohol), the points are shifted and seem to curve slightly, as does the smoothing line. I wonder what non-linear function could be used to transform the plot to a linear form?

Density vs. Residual Sugar

The first plot with all data points shows a tight concentration in the lower left quadrant and a few extreme outliers. The second plot zooms in and provides a good picture of the relationship between density and residual sugar (RS): wines with higher RS also have higher levels of density. The correlation coefficient for this pair is 0.84, indicating a very strong relationship.

Residual Sugar vs. Alcohol

In the first plot we see that there is a large concentration of wines with very low levels of residual sugar (RS). Zooming in, the second plot shows only those wines with RS levels below 23 g/dm³, and there is still a tight group of wines with very low RS levels at all levels of alcohol. This makes sense, as fermentation can only continue in the prescense of sugars, and different types of grapes will have differing levels of sugars (fructose and glucose) to begin with ⁵. As alcohol is produced, RS will decrease. The correlation coefficient for these variables was found to be -0.45, which is moderate.

Sweetness Level vs. Alcohol

This is related to the previous plots for residual.sugar vs. alcohol, as the sweetness level is a factorised variable based on residual sugar. The boxplot shows the relationship between alcohol and sweetness level: the median value for Dry wines is the highest at about 11, and it’s IQR is about the same as for Medium-Dry wines. The distribution of Medium wines has a much narrower IQR and more outliers in it’s long tail.

Density vs. Total Sulfur Dioxide

The first plot shows a tight concentration of points in the lower left quadrant trending in an upward slant with a few outliers. Zooming in on this main area, there is a good sense of following a line: as total sulfur dioxide increases density also increases. A coefficient of 0.53 between density and total sulfur dioxide indicates a moderate correlation.

Total Sulfur Dioxide vs. Alcohol

Zooming in on the loose mass of points in the second plot, and removing 6 outliers, there is a hint of a relationship which reflects a moderate correlation of -0.45 between alcohol and total sulfur dioxide; as levels of total sulfur dioxide increase, alcohol levels tend to decrease.

Volatile Acidity vs. Residual Sugar

The plot shows a tight concentration of points in the lower left quadrant with a few outliers. Zooming in on this main area we see the mass of points is not structured or organized in any linear or uniform way. This reflects the essentially zero correlation of 0.06 between residual sugar and volatile acidity.

Quality Level vs. Total Sulfur Dioxide

I’m going to use the simplified quality level variable here instead of the quality factors to see if there’s anything here.

## df$quality.level: poor
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     9.0   117.0   149.0   148.6   182.0   440.0 
## -------------------------------------------------------- 
## df$quality.level: good
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    18.0   107.2   132.0   137.0   164.0   294.0 
## -------------------------------------------------------- 
## df$quality.level: excellent
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    34.0   101.0   122.0   125.2   146.0   229.0

## 
##  Pearson's product-moment correlation
## 
## data:  as.numeric(df$quality.level) and df$total.sulfur.dioxide
## t = -14.371, df = 4896, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2279069 -0.1741594
## sample estimates:
##        cor 
## -0.2011845

The scatter plot shows a wider variance of total sulfur dioxide levels (TSO2) for poor quality wines; the interquantile range (IQR) is over 65 g/L compared to about 45 for excellent quality wines. The faint downward slope of the smoothing line suggests that there really isn’t any relation here; the correlation coefficient for the pair is -0.20.

Quality vs. Volatile Acidity

Volatile acidity shows similar tendencies as for total sulfur dioxide: a vague hint of a trend, the correlation coefficient of -0.20 is extremely weak. The second boxplot displays the distribution of wines with higher-VA: although there are few of these, the medians are all very close.

The scatter plot shows the very shallow slope, reflecting the weak correlation.

When using the simplified quality levels, poor, good and excellent, we have this plot.

## df$quality.level: poor
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1000  0.2400  0.2900  0.3103  0.3500  1.1000 
## -------------------------------------------------------- 
## df$quality.level: good
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0800  0.2000  0.2500  0.2606  0.3000  0.9650 
## -------------------------------------------------------- 
## df$quality.level: excellent
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0800  0.1900  0.2500  0.2653  0.3200  0.7600

There really isn’t much difference between poor and excellent.

Quality vs. Citric Acid

The boxplot shows little variation in the median across quality scores, and the variance for quality 6 and 5 can be explained by the fact that there are far more wines in these categories. With an upper limit set at 0.75 in the scatter plot, we can see the distributions more clearly. It doesn’t look like there is any trend here for citric acid, reflecting the low correlation value of -0.17.

Chlorides vs. Alcohol

In the first plot we see that there is a large concentration of wines with low levels of chlorides. In the second plot, a limit of 0.08 g/dm³ is set on the x-axis, and this smoothing line appears to be pulled out of alignment with the mass of points. The correlation coefficient for these variables was found to be -0.36, which is quite weak, even though the bulk of the points does suggest something of a trend.

Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?

The attribute with the highest correlation with the quality score is alcohol, and this is only a moderate correlation. Alcohol does have a strong correlation with density, and density, in turn, has an even stronger correlation with residual sugar (RS).

From the plots so far, it looks like wines with higher quality scores tend to have higher levels of alcohol. Looking just at the categories with higher counts of wines, the median level of alcohol for quality 5 wines is about 9.5 (%/volume) while it’s about 10.5 for quality 6 wines and 11.5 for quality 7 wines. Using the simplified categories gives us similar results, the medians are about 9.5 for poor and 11.5 for excellent.

Wine with higher density has higher levels of residual sugar (RS) and lower levels of alcohol. These relationships with density are highly correlated, reflecting the main processes involved in fermentation.

It is interesting, despite a weak correlation between alcohol and RS, there does appear to be a trend that as RS increases, alcohol decreases.

Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?

Even though total sulfur dioxide (TSO2) is moderately correlated with density, there is a hint that wines having higher levels of TSO2 tend to have a higher density. This makes sense from a molecular standpoint!

The relationship between alcohol and chlorides looks interesting; one area of the plot looked quite organized, while there were a large number scattered loosely further out.

What was the strongest relationship you found?

The strongest relationships were between density and residual sugar, with a strong positive correlation of 0.84, and between density and alcohol, with a strong negative correlation of -0.78.

Alcohol

In these density plots we see that the highest quality wines (9) have a much higher tendency to have high levels of alcohol, and the poorest quality tend to have the lowest. In the plot with simplified quality levels - excellent, good and poor - the combined group of excellent quality wines (7-9) still do tend to have higher alcohol levels, and that the poor(er) quality wines (3-5) also stilll have a greater tendency to have low alcohol levels.

Sweet wines are predominantly associated with lower alcohol levels, and Dry wines tend to have higher alcohol levels than Medium wines.

It looks like most of the wines with high levels of free sulfur dioxide (high_SO2 is above 50 ppm) tend to have lower alcohol levels. For wines with lower free SO2 levels, there is not much variance across levels of alcohol.

For volatile acidity (VA), there’s not much difference between higher-VA and lower-VA wines, both categories show similar distributions.

Density

Here we see how the distribution for wine density differs between poor and excellent quality wines, it’s essentially the same as the violin plot seen in the previous Bivariate Plots section. Within the excellent wines group, there are proportionately more with lower densities, while the other groups exhibit more balanced proportions.

The differentiation by sweetness level is more pronounced, Dry wines have a tendency to have lower densities, while Medium sweetness wines have higher densities.

Residual Sugar

(NOTE: I’ve set an upper limit of 23 g/dm³ for residual sugar levels to remove outliers.) All quality levels have a tendency to have lower residual sugar, the excellent more so than the others. This is expected though, as about 43% of the wines in the dataset are in the Dry category.

Density vs. Alcohol

Quality vs. Alcohol

Quality vs. Density

Quality/Alcohol

I want to look at the ratio of quality score to alcohol level, as alcohol is the most correlated with quality score.

The boxplot shows the distributions of the quality/alcohol ratios for each quality score. The medians for the quality/alcohol ratios increase across for quality scores, as expected.

The density plot for the quality/alcohol ratio by quality score shows a similar distinction in variations as the boxplot; the wines with the lower scores have similar tendencies to have low quality/alcohol ratios. As quality score increases, the quality/alcohol ratio varies more, but the tendency is that the ratio is higher than the previous score.

The variation between sweetness levels is minimal.

## # A tibble: 4 x 9
##   sweetness.level Count  Min. Qu_1st Median  Mean Qu_3rd  Max.       SD
##   <fct>           <int> <dbl>  <dbl>  <dbl> <dbl>  <dbl> <dbl>    <dbl>
## 1 Dry              2097 0.242  0.492  0.541 0.543  0.594 0.909   0.0772
## 2 Medium-Dry       1975 0.238  0.522  0.556 0.563  0.612 0.865   0.0722
## 3 Medium            825 0.273  0.543  0.588 0.612  0.667 0.941   0.0958
## 4 Sweet               1 0.513  0.513  0.513 0.513  0.513 0.513 NaN

The medians and IQRs for the ratio of quality to alcohol doesn’t seem to vary a great deal between sweetness levels, although the Dry wines do have the lowest median. Medium-Dry wines have the least variation, while Medium wines have the largest.

##                              [,1]
## fixed.acidity        -0.017260785
## volatile.acidity     -0.260100374
## citric.acid           0.054551345
## residual.sugar        0.277082877
## chlorides             0.069552184
## free.sulfur.dioxide   0.205198540
## total.sulfur.dioxide  0.176955861
## density               0.314650471
## pH                   -0.009481407
## sulphates             0.064787558
## alcohol              -0.346440167
## quality               0.686868666

Standard deviation is not calculated for Sweet wines as there is only 1. It looks like this variable does not correlate with the other features of the dataset.

Quality/Alcohol vs. Density

This plot shows distinct, slightly overlapping bands for the quality scores. For any level of density, the pattern of quality scores seems to be regular: higher quality wines have higher quality/alcohol ratios and predominantly lower density levels. Wines with the lowest quality/alcohol ratios also have the lowest quality scores.

For excellent wines, as the quality/alcohol ratio increases, the density also tends to increase. Poor quality wines generally have lower quality/alcohol ratios and slightly higher densities.

Alcohol vs. Volatile Acidity

Total Sulfur Dioxide

The density distributions for total sulfur dioxide (TSO2) indicate that excellent quality wines have a stronger tendency to have lower levels of TSO2 than poor quality wines.

Similarily, Dry wines have a tendency to have lower TSO2 levels than do Medium sweet wines.

Density vs. Total Sulfur Dioxide

Density and total sulfur dioxide (TSO2) are moderately correlated with a coefficient of 0.53, so I want to look at how they relate.

Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?

If we ignore the single Sweet wine, as it could be considered an outlier (and is the only one in its group), we see that Dry wines have the lowest median for quality/alcohol ratio (quality per alcohol % by volume). This does make sense, as the Dry wines have a tendency to have higher alcohol levels than the other levels, and poor wines have a far greater tendency to have low alcohol levels. The variance is similar for Medium-Dry wines, but greater for Medium wines; standard deviation and IQR are both larger.

The quality vs. alcohol plots show that for Dry and Medium-Dry wines the quality level increases at the same time as alcohol levels increase. This pattern does not hold for Medium wines; most of them are in the lower alcohol levels, and not many in the higher quality range.

When we compare the characteristics of wines of a specific alcohol level (holding alcohol level constant), wines with lower density have higher quality scores.

Were there any interesting or surprising interactions between features?

The density vs. alcohol levels showed distinct bands between sweetness levels. This makes sense as there is a high correlation between density and residual sugar, on which the sweetness levels are based.

At higher levels of volatile acidity, there is a separation in wine scores; holding VA constant (for example at 0.4), wines with higher alcohol levels have higher quality scores.

OPTIONAL: Did you create any models with your dataset? Discuss the strengths and limitations of your model.

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Plot One

Description One

The distribution of alcohol (% by volume, or ABV) levels in the white wines has a very exaggerated positive skew, with the median at 10.4, in the lower half of the range.

Plot Two

Description Two

White wines with the highest quality score have the highest median ABV, and the median increases as quality score increases from 5 and up. The variance for the lower quality ratings are similar to each other.

For wines with lower scores, there is a similar tendency to have low quality/alcohol ratios. The highest quality score has a much greater tendency to have the highest quality/alcohol ratio.

Plot Three

Description Three

There are distinct, slightly overlapping bands for the quality scores. Holding density constant, the quality score increases as quality/alcohol ratio increases. The bands of quality scores (colours) seem to separate more as density increases.